Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[[re, im] = \mathsf{sort}([re, im]) \\]
\[re \cdot im + im \cdot re \]
↓
\[\left(re + re\right) \cdot im \]
re \cdot im + im \cdot re
↓
\left(re + re\right) \cdot im

(FPCore im_sqr (re im) :precision binary64 (+ (* re im) (* im re)))
↓
(FPCore im_sqr (re im) :precision binary64 (* (+ re re) im))
double im_sqr(double re, double im) {
	return (re * im) + (im * re);
}
↓
double im_sqr(double re, double im) {
	return (re + re) * im;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot im + im \cdot re \]

  2. Simplified0.0

    \[\leadsto \color{blue}{re \cdot \left(im + im\right)} \]

  3. Applied *-un-lft-identity_binary640.0

    \[\leadsto re \cdot \left(im + \color{blue}{1 \cdot im}\right) \]

  4. Applied distribute-rgt1-in_binary640.0

    \[\leadsto re \cdot \color{blue}{\left(\left(1 + 1\right) \cdot im\right)} \]

  5. Applied associate-*r*_binary640.0

    \[\leadsto \color{blue}{\left(re \cdot \left(1 + 1\right)\right) \cdot im} \]

  6. Simplified0.0

    \[\leadsto \color{blue}{\left(re + re\right)} \cdot im \]

  7. Final simplification0.0

    \[\leadsto \left(re + re\right) \cdot im \]

Reproduce

herbie shell --seed 2022068 
(FPCore im_sqr (re im)
  :name "math.square on complex, imaginary part"
  :precision binary64
  (+ (* re im) (* im re)))